document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161014>Question 1161014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You owe your parents $27,000 (in present day dollars) and want to repay them in equal amounts the first to occur in 3 years from today and the other in 8 years from today. If the interest rate is 6.1% per annum compounding monthly, what will be the amount of each repayment?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784558 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=784558\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> to make this easier for you to see, i've assigned letters to the numbers.<BR>\n" );
document.write( "you can then replace the letters with numbers to determine for yourself that the answer is the answer i gave you.\r<BR>\n" );
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document.write( "let a = (1 + .061/12) ^ 36<BR>\n" );
document.write( "let b = (1 + .061/12) ^ 96<BR>\n" );
document.write( "let x = the amount you are looking for.\r<BR>\n" );
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document.write( "x/a is the present value of the payment in the 48th month (4th year).<BR>\n" );
document.write( "x/b is the present value of the payment in the 96th month (8th year).\r<BR>\n" );
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document.write( "your formula is x/a + x/b = 27000.<BR>\n" );
document.write( "multiply both sides of this formula by a*b to get:<BR>\n" );
document.write( "a*b*x/a + a*b*x/b = a*b*27000<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "b*x + a*x = a**b*27000<BR>\n" );
document.write( "factor out the x on the left side of the equation to get:<BR>\n" );
document.write( "x*(a+b) = a*b*27000<BR>\n" );
document.write( "divide both sides of the equation by (a+b) to get:<BR>\n" );
document.write( "x = a*b*27000/(a+b)\r<BR>\n" );
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document.write( "your answer will be 18649.41705 \r<BR>\n" );
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document.write( "that's the payment in the 48th month and the 96th month that will satisfy the 27000 loan.\r<BR>\n" );
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document.write( "the present value of that for 36 months = 18649.41705 / (1 + .061/12) ^ 36 = 15537.84162.<BR>\n" );
document.write( "the present value of that for 96 months = 18649.41705 / (1 + .061/12) ^ 96 = 11462.15838.<BR>\n" );
document.write( "their sum = 27000 which is the present value of the loan.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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